Method and apparatus for testing ic

ABSTRACT

A testing method includes measuring an electrical parameter of a device under test (DUT) and a corresponding temperature of the DUT one or more times, determining coefficients in a pre-constructed model based on a plurality of measured values of the electrical parameter and corresponding measured temperatures to characterize a relationship of the electrical parameter to the temperature, and determining a quality of the DUT based on the model and a limit value of the electrical parameter at a specified temperature. The model is pre-constructed to characterize the relationship of the electrical parameter to the temperature with the coefficients that are DUT-dependent variables.

INCORPORATION BY REFERENCE

This present disclosure claims the benefit of U.S. ProvisionalApplications No. 61/445,839, “Parametric Temperature Adjustment DuringIC Testing” filed on Feb. 23, 2011, and No. 61/507,916, “Adjustingfrequency measurement on ATE due to Temperature Fluctuation”, filed onJul. 14, 2011, which are incorporated herein by reference in theirentirety.

BACKGROUND

The background description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent the work is described in thisbackground section, as well as aspects of the description that may nototherwise qualify as prior art at the time of filing, are neitherexpressly nor impliedly admitted as prior art against the presentdisclosure.

Electrical parameters of electrical circuits, such as currentconsumption, maximum working frequency, and the like, are tested todetermine quality of the circuit based on measured values. Theelectrical parameters can be sensitive to temperature. Thus, temperaturefluctuation can affect the measured values, and change test results.

SUMMARY

Aspects of the disclosure provide a method for testing. The methodincludes measuring an electrical parameter of a device under test (DUT)and a corresponding temperature of the DUT one or more times,determining coefficients in a pre-constructed model based on a pluralityof measured values of the electrical parameter and correspondingmeasured temperatures to characterize a relationship of the electricalparameter to the temperature, and determining a quality of the DUT basedon the model and a limit value of the electrical parameter at aspecified temperature. The model is pre-constructed to characterize therelationship of the electrical parameter to the temperature with thecoefficients that are DUT-dependent variables.

To determine the quality of the DUT, in an embodiment, the methodincludes determining a value for the electrical parameter at thespecified temperature according to the model, and comparing thedetermined value to the limit value to determine the quality of the DUT.In another embodiment, the method includes determining a temperaturevalue at which the DUT has the limit value of the electrical parameteraccording to the model, and comparing the determined temperature valueto the specified temperature to determine the quality of the DUT.

According to an aspect of the disclosure, to measure the electricalparameter of the DUT and the corresponding temperature of the DUT, themethod includes testing the DUT according to a test flow that includes aplurality of parametric tests inserted in a sequence of other tests, andmeasuring the electrical parameter of the DUT and the correspondingtemperature in response to each of the parametric tests.

Aspects of the disclosure provide a test system. The test systemincludes an interface and a controller. The interface is configured tomeasure an electrical parameter of a device under test (DUT) and acorresponding temperature of the DUT. The controller is configured tocontrol the interface to measure the electrical parameter of the DUT andthe corresponding temperature of the DUT one or more times, determinecoefficients in a pre-constructed model based on the measured values ofthe electrical parameter and the corresponding measured temperatures tocharacterize a relationship of the electrical parameter to thetemperature, and determine a quality of the DUT based on the model and alimit value of the electrical parameter at a specified temperature. Themodel is pre-constructed to characterize the relationship of theelectric parameter to the temperature with the coefficients that areDUT-dependent variables.

Aspects of the disclosure provide another method for testing anintegrated circuit product. The method includes constructing a model formodeling an electrical parameter of a device changing with atemperature. The model includes a plurality of coefficients that aredevice-under-test (DUT) dependent variables. Further, the methodincludes determining an integer number that the integer number ofmeasurements of the electrical parameter and the correspondingtemperature provides a suitable indication of the device meeting theelectrical parameter at a specified temperature that is not measured.Then, the method includes performing, for at least the integer number oftimes on a DUT, a parametric test measuring the electrical parameter andthe corresponding temperature, and ascertaining a quality of the DUT tomeet a threshold at a non-measured temperature based on the model andthe parametric test.

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments of this disclosure that are proposed as exampleswill be described in detail with reference to the following figures,wherein like numerals reference like elements, and wherein:

FIG. 1 shows a block diagram of a test system example 100 according toan embodiment of the disclosure;

FIG. 2 shows a flow chart outlining a process example 200 for generatinga test flow according to an embodiment of the disclosure;

FIG. 3 shows a flow chart outlining a process example 300 for testing acircuit according to an embodiment of the disclosure;

FIGS. 4A and 4B show plots of parameters vs. temperature according to anembodiment of the disclosure;

FIGS. 5A and 5B show plots of temperature variation during a test flowaccording to an embodiment of the disclosure;

FIGS. 6A and 6B show plots for a frequency to temperature modelaccording to an embodiment of the disclosure; and

FIG. 7 shows a flow chart outlining a process example 700 for testing acircuit according to an embodiment of the disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS

FIG. 1 shows a block diagram of a test system example 100 according toan embodiment of the disclosure. The test system 100 includes automatictest equipment (ATE) 150 and device under test (DUT) 110. The ATE 150and the DUT 110 are suitably coupled together via a prober or a handler,for example. The ATE 150 acts on the DUT 110 according to a test flow160, and receives test results. A quality of the DUT 110, that is itsfitness to meet specified performance requirements, is then determinedbased on the test results.

According to an embodiment of the disclosure, the test flow 160 includesa plurality of parametric tests (PT) 161 that are separated by othertests, such as I/O test, CPU test, memory test, and the like. Each PT161 performs a measurement of one or more electrical parameters, such ascurrent consumption, an operational frequency, and the like. Because ofcorrespondence between the electrical parameter and temperature,temperature is also measured. Based on the measurements of theelectrical parameters (e.g., P1, P2) and the corresponding measurementsof the temperature (e.g., T1, T2), the quality of the DUT 110, and morespecifically its fitness to a meet a performance specification, isdetermined.

In an embodiment, the quality of the DUT 110 is determined based on alimit value of an electrical parameter at a specified temperature(T_(SPEC)). In an embodiment, the corresponding temperatures (e.g., T1,T2) at which the electrical parameters are measured are not the same asa temperature (T_(SPEC)) that is specified in a product datasheetspecification. Instead, in an embodiment, the ATE 150 calculates a valueof the electrical parameter at the specification temperature (T_(SPEC))based on the measurements of the electrical parameter (e.g., P1, P2) atone or more temperatures (e.g. T1, T2) that are different from thespecification temperature (T_(SPEC)). Then, the ATE 150 compares thecalculated value to the limit value of the electrical parameter todetermine the quality of the DUT 110.

The DUT 110 can be any suitable device. In an embodiment, the DUT 110 isone of a plurality of integrated circuit (IC) chips on a wafer. Inanother embodiment, the DUT 110 is an IC package that includes an ICchip and other circuit components, such as a ball grid array substrateor other suitable circuit interface, and an encapsulation medium.

According to an embodiment of the disclosure, the DUT 110 includes atemperature sensor 120 that is configured to measure a temperature. Inan example, the temperature sensor 120 includes a circuit component,such as a diode or other suitable temperature measuring circuitry on theIC chip to measure an on-chip temperature. In an example, diode currentis indicative of a junction temperature. In another example, U.S. Pat.No. 7,726,877 discloses Method and Apparatus of Measuring Temperature,the disclosure of which is incorporated by reference in its entirety.

It is noted that, in another example, the temperature sensor 120 is anoff chip component to measure the chip temperature. In an example, thetemperature sensor 120 is in contact with the IC chip. In anotherexample, the temperature sensor 120 is in a close proximity to the ICchip to measure a chip temperature. In another example, the temperaturesensor 120 is not need to be in the close proximity to the IC chip tomeasure the chip temperature.

According to an embodiment of the disclosure, a temperature profile of aDUT 110 changes due to various factors, such as process variation,handler to handler variation, handler setup, device order and the like.In an example, a first DUT 110 starts a test at 85° C., and finishes thetest at 140° C.; and a second DUT 110 starts a test at 95° C., andfinishes the test at 80° C.

Further, electrical parameters are sensitive to temperature. Forexample, a first measurement of the static current consumption of a DUT110 at a relatively higher temperature can be larger than a secondmeasurement of the static current consumption of the same DUT 110 at arelatively lower temperature. Thus, in an embodiment, comparingmeasurements to the limit value without considering the temperature ofthe DUT 110 at the time of the measurement can lead to undesirableconsequence, such as high yield loss or customer returns.

However, adjusting the temperature of the DUT 110 to the specifiedtemperature can be time consuming and increase test time and cost.According to an embodiment of the disclosure, the test system 100 isconfigured to determine the value of the electrical parameter at aspecified temperature (T_(SPEC)) based on a pre-constructed model andparametric measurements of electrical parameters at temperatures otherthan at the specified temperature (T_(SPEC)).

According to an aspect of the disclosure, the ATE 150 includes acontroller 170, and an interface 151. The interface 151 includes anysuitable components, such as pin electronics, pin driver, pin sensor,parametric measurement unit (PMU), and the like, that can operate on theDUT 110 to perform test. In an example, a PMU is configured to applyvoltage at a pin and measure current at the same pin. The controller 170controls the interface 151 to operate on the DUT 110 according to thetest flow 160, receives test results from the interface 151, anddetermines the quality of the DUT 110 based on the test results.

According to an embodiment of the disclosure, the test flow 160 includesa plurality of parametric tests 161 that are inserted at differentpositions in the sequence of the tests. According to an aspect of thedisclosure, the DUT 110 consumes power during test, and may heat upitself, thus the temperature of the DUT 110 can be different at thedifferent positions in the test, and in an embodiment the temperature ofthe DUT 110 is different than the temperature at which the limit valueof the electric parameter is specified in a product datasheetspecification. In an example, an I/O test consumes relatively low power,and the temperature of the DUT 110 during and immediately after I/O testis relatively low. The CPU test and the memory test consume relativelylarge power and the temperature of the DUT significantly increasesduring the CPU test and the memory test. The positions of the pluralityof parametric tests 161 in the test flow 160 can be selected thattemperatures of the DUT 110 at the plurality of parametric tests 161have a relatively large variation. Although the temperatures at whichthe electrical parameter of the DUT 110 is actually tested deviate fromthe specified temperature, in an embodiment, a value of the electricalparameter for the DUT 110 at the specified temperature is derived basedon actual measurements of the electrical parameter and a modelcharacterizing performance of the DUT.

In an example, the test flow 160 is implemented in the form of a testsoftware program. For example, each test is a module or a function inthe test software program. The controller 170 is implemented as aprocessor executing software programs. The processor executes the testsoftware program and controls the interface 151 to sequentially act onthe DUT 110 to perform the sequence of tests. In response to aparametric test 161, the interface 151 acts on the DUT 110 to measureone or more electrical parameters and to measure a temperature of theDUT 110.

Further, the controller 170 receives measured values of the electricalparameter with corresponding temperatures. In an example, the controller170 receives a first measured value of the electrical parameter andcorresponding temperature (P1, T1) in response to a first parametrictest 161, and receives a second measured value of the electricalparameter and corresponding temperature (P2, T2) in response to a secondparametric test 161.

In addition, in an embodiment, the controller 170 employs apre-constructed model characterizing the relationship of the electricalparameter and the temperature. The pre-constructed model may have one ormore unknown coefficients. In an example, the coefficients are DUTdependent such that different DUTs may have different coefficients.Based on one or more measured value of the electrical parameter and thecorresponding temperature of the DUT 110, the controller 170 determinesthe coefficients for the DUT 110.

Further, the controller 170 determines a value of the electricalparameter at the specified temperature (T_(SPEC)) according to themodel, even though the electrical parameter was tested at temperaturesother than the specified temperature. For example, the controller 170uses the model with the solved coefficients to calculate the value ofthe electrical parameter at the specified temperature for the DUT 110.Then, the controller 170 determines the quality of the DUT 110 based onthe determined value. In an example, the controller 170 sorts the DUT110 into different bins, such as a high speed bin, a typical bin, a lowspeed bin, and the like, based on the determined value. In anotherexample, the controller 170 determines pass or fail based on thedetermined value.

FIG. 2 shows a flow chart outlining a process example 200 for generatinga test flow, such as the test flow 160 according to an embodiment of thedisclosure. The process starts at S201 and proceeds to S210.

At S210, a prototype model that models, or characterizes, an electricalparameter as a function of temperature is determined. In an example, apolynomial model, such as a linear model, a quadratic model, and thelike, is determined to model an electrical parameter changing withtemperature. In another example, a non-polynomial model is determined tomodel an electrical parameter changing with temperature. The model caninclude coefficients that are DUT dependent variables.

In an embodiment, multiple DUTs are selected to undergo acharacterization process to characterize the electrical parameterchanging with the temperature. During the characterization process, foreach DUT, the electrical parameter is measured at various differenttemperatures. Based on the characterization, the prototype model isconstructed.

At S220, a plurality of inserting points in a test flow is selected. Inan example, for a linear model, at least two inserting points in a testflow are selected. For example, one of the two inserting points isimmediately after an I/O test following which the DUT is expected tohave a relatively low temperature, and another inserting point is afterone or more high power consuming tests, such as after a memory testand/or CPU test that are expected to significantly raise the temperatureof the DUT. Thus, the two inserting points have a relatively largetemperature differential.

In another example, for a quadratic model, at least three insertingpoints in a test flow are selected. For example, a first of the threeinserting points is immediately after an I/O test following which theDUT is expected to have a relatively low temperature, a second of thethree inserting points is immediately after one of the high powerconsuming tests, following which the DUT is expected to have arelatively higher temperature than after the I/O test, and a third ofthe three inserting points is after completion of all of the high powerconsuming tests following which the DUT is expected to have an evenhigher temperature.

At S230, parametric tests are inserted in the test flow at the selectedinstering points to form a new test flow. Then, the new test flow isused to test DUTs. The process then proceeds to S299 and terminates.

According to an embodiment of the disclosure, the process 200 isperformed by a processor to automatically generate the new test flow.

FIG. 3 shows a flow chart outlining a process example 300 for testequipment, such as ATE 150, to test a circuit according to an embodimentof the disclosure. The process starts at S301 and proceeds to S310.

At S310, the ATE 150 tests the DUT 110 according to the test flow 160.In an embodiment, the test flow 160 includes a sequence of tests, andthe sequence of tests includes a one or more parametric tests 161.According to an embodiment of the disclosure, the positions to insertthe one or more parametric tests 161 can be selected such thattemperatures of the DUT under the plurality parametric tests 161 have arelatively large variation. In an example, in response to a parametrictest 161, the interface 151 acts on the DUT 110 to measure one or moreelectrical parameters and to measure a temperature of the DUT 110 whenthe electrical parameters are measured.

At S320, the ATE 150 receives measured values of the electricalparameter with corresponding temperature. In an example, the ATE 150receives a first measured value of the electrical parameter andcorresponding temperature (P1, T1) in response to a first parametrictest 161, and receives a second measured value of the electricalparameter and corresponding temperature (P2, T2) in response to a secondparametric test 161.

At S330, the ATE 150 determines coefficients in a pre-constructed modelfor a circuit type to which the DUT corresponds. According to anembodiment of the disclosure, the pre-constructed model characterizes arelationship of the electrical parameter to temperature. Thepre-constructed model includes unknown coefficients. In an example, thecoefficients are DUT dependent.

In an embodiment, the polynomial model is pre-constructed to modelbehavior of the electrical parameter changing as a function oftemperature within a temperature range. The polynomial model includesunknown coefficients. Based on the received values of the electricalparameter with the corresponding temperatures, the unknown coefficientsare solved.

In an example, when the polynomial model is a linear model, the linearmodel has two unknown coefficients. In an example, the two coefficientscan be solved based on measurements of two parametric tests, using anysuitable technique, such as an algebraic technique, matrix calculation,and the like. In another example, the two coefficients can be solvedbased on measurements of more than two parametric tests, using curvefitting, for example.

At S340, the ATE 150 determines a value of the electrical parameter at aspecified temperature according to the model. In an example, the qualityof the DUT 110 is determined using a limit value of the electricalparameter at the specified temperature. In an example, a productdatasheet specification specifies a lower limit value of the electricalparameter at the specified temperature. Then, when the electricalparameter of a DUT at the specified temperature is higher than the lowerlimit value, the DUT satisfies the product datasheet specification; andwhen the electrical parameter of the DUT at the specified temperature islower than the lower limit value, the DUT fails the product datasheetspecification. The ATE 150 uses the model to derive the value of theelectrical parameter at the specified temperature for the DUT 110. Thus,while the parametric tests 161 are not performed at the specifiedtemperature, the measured values for the electrical parameters withcorresponding temperatures can be used to predict the value of theelectrical parameter of the DUT 110 at the specified temperature.

At S350, the ATE 150 determines the quality of the DUT 110 based on thederived value. In an embodiment, the ATE 150 makes pass or fail decisionof the DUT 110 based on the derived value. In an example, the ATE 150compares the derived value with the limit value to make the decision. Inanother embodiment, the ATE 150 sorts the DUT 110 into different bins,such as a high speed or fast bin, a regular speed or typical bin, a lowspeed or slow bin, and the like, based on the derived value. Then theprocess proceeds to S399 and terminates.

FIG. 4A shows a plot 400A of an electrical parameter (PARA-1)characterization according to an embodiment of the disclosure. In FIG.4A, the X-axis indicates temperature, and the Y-axis indicates ameasured value of the electrical parameter (PARA-1). The plot 400Aincludes a first curve 410A, a second curve 420A and a third curve 430A.In an example, the first curve 410A corresponds to measurements on afirst device in a characterization process, the second curve 420Acorresponds to measurements on a second device in the characterizationprocess, and the third curve 430A corresponds to measurements on a thirddevice in the characterization process.

During the characterization process, in an embodiment, a plurality ofdevices, such as the first, second and third devices, are selected andcharacterized to determine a suitable model to model PARA-1 changingwith temperature. In an example, the first, second and third devicescorrespond to fast, regular and slow devices. Then, a thermal source,such as a heat source, a heat sink, and the like is controlled to changethe temperature on the devices. Further, PARA-1 of the device andcorresponding temperature of the device are measured at varioustemperatures, such as temperatures in a range. Based on themeasurements, the curves 410A-430A can be plotted, and a model can beconstructed. In the FIG. 4A example, a quadratic model can be selectedto model PARA-1 changing with temperature in the temperature range, suchas the quadratic model in Eq. 1.

PARA-1=α₀+α₁ ×T+α ₂ ×T ²   Eq. 1

In an example, the quadratic model includes three variable coefficients,such as α₀, α₁, and α₂ in Eq. 1, that are device dependent.

FIG. 4B shows a plot 400B of an electrical parameter (PARA-2)characterization according to an embodiment of the disclosure. TheX-axis is temperature, and the Y-axis is measured value of theelectrical parameter (PARA-2). The plot 400B includes a first curve410B, a second curve 420B and a third curve 430B. In the FIG. 4Bexample, a linear model can be selected to model PARA-2 changing withtemperature in the temperature range, such as the liner model in Eq. 2.

PARA-2=b ₀ +b ₁ ×T   Eq. 2

In an example, the linear model includes two variable coefficients, suchas b₀ and b₁ in Eq. 2, that are device dependent.

FIG. 5A shows a plot 500A of temperature variation during a test flowaccording to an embodiment of the disclosure. The test flow includes asequence of various tests. In the FIG. 5A example, the test flow startswith I/O test. The I/O test is followed by CPU test and memory test.

According to an embodiment of the disclosure, during test, a DUTconsumes power, and portion of the power is converted to heat and heatsup the DUT. In an example, I/O test consumes relatively low power, andthe temperature increase of the DUT during I/O test is relatively low,The CPU test and the memory test consume relatively large power and thetemperature of the DUT significantly increases during the CPU test andthe memory test.

According to an embodiment of the disclosure, a DUT is tested accordingto the test flow, and the temperature of the DUT is monitored during thetest. In the FIG. 5A example, a curve 520 shows a temperature profilefor the DUT during the test.

Further, according to an embodiment of the disclosure, the temperatureprofile can be different due to, for example, handler to handlerdifferences, handler setup, device order, start up temperature, and thelike. In an embodiment, a plurality of DUTs is tested according to thetest flow, and the temperature of the plurality of DUTs is monitoredduring the test. In an example, the plurality of DUTs can be selectedfrom dies on different locations of a wafer, dies from different wafers,and dies from different lots. Further, the plurality of DUTs can betested using different test equipment.

In the FIG. 5A example, the temperature of the plurality of DUTs changesbetween an upper curve 510 and a lower curve 530.

In an embodiment, according to the temperature profile, a plurality ofinserting points in the test flow can be selected to insert parametrictests. For example, to solve three coefficients in the quadratic modelthat models PARA-1 in FIG. 4A, three inserting points are selected toinsert parametric tests (PARA-1_TEST) 550. Each parametric test 550measures PARA-1 of a DUT and a corresponding temperature of the DUT atthe time of the parametric test 550. In an embodiment, one or more of afrequency parameter and current consumption parameter of a DUT ismeasured at each of the parametric test 550, for example.

It is noted that more than three inserting points can be selected toinsert parametric tests in the test flow. However, parametric tests alsoconsume test time, and a large number of parametric tests can alsoincrease test cost and thus increase chip or device cost.

FIG. 5B is similar to FIG. 5A. To solve the two coefficients of thelinear model that models PARA-2 in FIG. 4B, two inserting points areselected to insert parametric tests (PARA-2_TEST) 560. Each parametrictest 560 measures PARA-2 of a DUT and a corresponding temperature of theDUT at the time of the parametric test 560. In an embodiment, one ormore of a frequency parameter and current consumption parameter of a DUTis measured at each of the parametric test 560, for example

It is noted that more than two inserting points can be selected toinsert parametric tests in the test flow. However, parametric tests alsoconsume test time, and a large number of parametric tests can alsoincrease test cost and thus increase chip or device cost.

According to an embodiment of the disclosure, a reduced number ofparametric tests are inserted in a test flow to reduce test cost. In anembodiment, a model that models maximum working frequency at thespecified temperature is determined. In an embodiment, a singlemeasurement of a parameter, such as maximum working frequency forexample, is made at any suitable temperature. The single measuredparameter is applied to a model characterizing the DUT to predict theparameter at a specified temperature that is different from thetemperature at which the parameter is measured.

Thus, in such embodiment a single frequency test is needed and can beinserted at any suitable location in a test flow. Because only onefrequency test is needed and the frequency test can be performed at anysuitable temperature, test time and test cost is reduced.

FIG. 6A shows a plot 600A of a maximum frequency (FREQ) characterizationaccording to an embodiment of the disclosure. The X-axis is temperature(T), and the Y-axis is measured value of a parameter, which in theexample is the maximum operating frequency (FREQ) at which the IC isfunctional. The plot 600A includes a first curve 610, a second curve620, and a third curve 630. In an example, the first curve 610corresponds to maximum frequency measurements on a first device in acharacterization process, the second curve 620 corresponds to maximumfrequency measurements on a second device in the characterizationprocess, and the third curve 630 corresponds to maximum frequencymeasurements on a third device in the characterization process.

During the characterization process, in an embodiment, a plurality ofdevices, such as the first, second and third devices, are selected andcharacterized to determine a suitable model to characterize maximumfrequency changing with temperature. In an example, the first, secondand third devices correspond to fast, typical and slow devices. Then, athermal source, such as a heat source, a heat sink, and the like iscontrolled to change the temperature on the devices. In another example,the first, second and third devices are randomly selected from differentwafers, different lots, and the like or are collected in a database overtime from testing numerous DUTs that include all process plurality.Further, measurements of the maximum frequency and correspondingtemperature is conducted at various temperatures, such as temperaturesin a range. Based on the measurements, the curves 610-630 can beplotted, and a model can be determined. In the FIG. 6A example, a linearmodel, such as Eq. 3 can be used to model the maximum frequency changingwith temperature.

FREQ(T)=Slope×T+B   Eq. 3

where Slope and B are coefficients. Slope is the slope of the linearmodel and B is the intercept of the linear model.

Further, according to an embodiment of the disclosure, the maximumfrequency at the specified temperature (T_(SPEC)) is a function of theslope of the linear model. FIG. 6B shows a plot 600B for characterizingthe slope

$\left( \left( \frac{{FREQ}}{T} \right) \right)$

and the maximum frequency at the specified temperature (FREQ@ T_(SPEC)).In an embodiment, the slope is a function of the maximum frequency atthe specified temperature, as shown by Eq. 4:

Slope=Func(FREQ(T _(SPEC)))   Eq. 4

In an example, a linear model is used to model the slope and the maximumfrequency at the specified temperature, as shown by Eq. 5

Slope=α×FREQ(T _(SPEC))+βEq. 5

where α and β are coefficients that can be determined based on thecharacterization in FIG. 6B.

Further, in an embodiment, when a maximum frequency (FREQ(T_(TEST))) ofa DUT is measured at a temperature (T_(TEST)), the relationship of themeasured frequency to the maximum working frequency at the specifiedtemperature (T_(SPEC)) can be expressed by Eq. 6 according to the linearmodel in Eq. 3:

FREQ(T _(SPEC))−FREQ(T _(TEST))=Slope×(T _(SPEC) −T _(TEST))   Eq. 6

Further, by replacing the Slope in Eq. 6 with the Eq. 5, the maximumworking frequency at the specified temperature can be calculated by Eq.7

$\begin{matrix}{{{FREQ}\left( T_{SPEC} \right)} = \frac{{{FREQ}\left( T_{TEST} \right)} + {\beta \times \left( {T_{SPEC} - T_{TEST}} \right)}}{1 - {\alpha \times \left( {T_{SPEC} - T_{TEST}} \right)}}} & {{Eq}.\mspace{14mu} 7}\end{matrix}$

Thus, in accordance with an embodiment, only a single frequencymeasurement at a suitable temperature, which can be different from thespecified temperature, is needed to determine the maximum workingfrequency at the specified temperature.

FIG. 7 shows a flow chart outlining a process example 700 for testequipment, such as the ATE 150 to test a circuit, such as the DUT 110,according to an embodiment of the disclosure. In this embodiment, thetest flow 160 includes a single parametric test 161, such as the oneafter the memory test, for testing a maximum working frequency. Theprocess starts at S701, and proceeds to S710.

At S710, in response to the single parametric test 161, the ATE 150measures a maximum frequency of the DUT 110.

At S720, in response to the single parametric test 161, the ATE 150 alsomeasures a temperature of the DUT 110 at the time of the parametrictest.

At S730, the ATE 150 determines whether the measured temperature islarger than the specified temperature for the DUT, and whether themeasured maximum working frequency is larger than the limit frequency.When both conditions are satisfied, the process proceeds to S770;otherwise, the process proceeds to S740.

At S740, the ATE 150 derives a predicted maximum working frequency atthe specified temperature, for example, according to Eq. 7.

At S750, the ATE 150 determines whether the predicted maximum workingfrequency at the specified temperature is larger than the limitfrequency. When the predicted maximum working frequency is larger thanthe limit frequency, the process proceeds to S770; otherwise, theprocess proceeds to S760.

At S760, the ATE 150 determines that the DUT fails the maximum frequencytest. The process proceeds to S799 and terminates.

At S770, the ATE 150 determines that the DUT passes the maximumfrequency test. The process proceeds to S799 and terminates.

It is noted that the process 700 can be suitably modified. In anexample, at S760, the ATE 150 further determines whether the DUTsatisfies another limit, such as a slower limit, for the maximumfrequency test, and bins the DUT as a slow device when the DUT satisfiesthe slower limit.

According to an embodiment of the disclosure, the DUT 110 includes anon-chip ring oscillator, the frequency of the ring oscillator isindicative of the maximum working frequency of the DUT 110. In themaximum frequency test, the ATE 150 measures the frequency of the ringoscillator.

According to another embodiment of the disclosure, the ATE 150 providesa clock signal to the DUT 110. During the maximum frequency test, theATE 150 steps up the frequency of the clock signal. At each step, theATE 150 performs function tests on the DUT 110 to determine whether theDUT 110 operates correctly. When the DUT 110 passes the functionaltests, the clock signal steps up; otherwise, the maximum frequency isdetermined to be the last clock frequency under which the DUT 110 passesfunctional testing.

While aspects of the present disclosure have been described inconjunction with the specific embodiments thereof that are proposed asexamples, alternatives, modifications, and variations to the examplesmay be made. Accordingly, embodiments as set forth herein are intendedto be illustrative and not limiting. There are changes that may be madewithout departing from the scope of the claims set forth below.

1. A method, comprising: measuring an electrical parameter of a deviceunder test (DUT) and a corresponding temperature of the DUT one or moretimes; determining coefficients in a pre-constructed model based on aplurality of measured values of the electrical parameter andcorresponding measured temperatures to characterize a relationship ofthe electrical parameter to the temperature, the model beingpre-constructed to characterize the relationship of the electricalparameter to the temperature with the coefficients that areDUT-dependent variables; and determining a quality of the DUT based onthe model and a limit value of the electrical parameter at a specifiedtemperature.
 2. The method of claim 1, wherein determining the qualityof the DUT based on the model and the limit value of the electricalparameter at the specified temperature further comprises: determining avalue for the electrical parameter at the specified temperatureaccording to the model; and comparing the determined value to the limitvalue to determine the quality of the DUT.
 3. The method of claim 1,wherein determining the quality of the DUT based on the model and thelimit value of the electrical parameter at the specified temperaturefurther comprises: determining a temperature value at which the DUT hasthe limit value of the electrical parameter according to the model; andcomparing the determined temperature value to the specified temperatureto determine the quality of the DUT.
 4. The method of claim 1, whereinmeasuring the electrical parameter of the DUT and the correspondingtemperature of the DUT for the plurality of times further comprises;testing the DUT according to a test flow that includes a plurality ofparametric tests inserted in a sequence of other tests; and measuringthe electrical parameter of the DUT and the corresponding temperature inresponse to each of the parametric tests.
 5. The method of claim 1,wherein determining the coefficients in the pre-constructed model basedon the plurality of measured values of the electrical parameter andcorresponding temperatures further comprises: determining thecoefficients in a pre-constructed polynomial model based on the measuredvalues of the electrical parameter and corresponding temperatures. 6.The method of claim 1, wherein measuring the electrical parameter of theDUT and the corresponding temperature of the DUT one or more timesfurther comprises: measuring the electrical parameter of the DUT and acorresponding junction temperature of the DUT.
 7. The method of claim 1,wherein measuring the electrical parameter of the DUT and thecorresponding temperature of the DUT one or more times furthercomprises: measuring at least one of an operating frequency, a currentconsumption and an oscillator frequency and the correspondingtemperature of the DUT.
 8. The method of claim 1, wherein measuring theelectrical parameter of the DUT and the corresponding temperature of theDUT one or more times further comprises: measuring an operatingfrequency of the DUT and the corresponding temperature of the DUT for asingle time.
 9. The method of claim 8, further comprising: determiningthe coefficients in the pre-constructed model based on the measuredvalue of the electrical parameter and the corresponding measuredtemperature.
 10. An integrated circuit (IC) chip that is testedaccording to the method of claim
 1. 11. A test system, comprising: aninterface configured to measure an electrical parameter of a deviceunder test (DUT) and a corresponding temperature of the DUT; and acontroller configured to control the interface to measure the electricalparameter of the DUT and the corresponding temperature of the DUT one ormore times, determine coefficients in a pre-constructed model based onthe measured values of the electrical parameter and the correspondingmeasured temperatures to characterize a relationship of the electricalparameter to the temperature, and determine a quality of the DUT basedon the model and a limit value of the electrical parameter at aspecified temperature, wherein the model is pre-constructed tocharacterize the relationship of the electric parameter to thetemperature with the coefficients that are DUT-dependent variables. 12.The test system of claim 11, wherein the controller is configured todetermine a value of the electrical parameter at the specifiedtemperature according to the model, and compare the value to the limitvalue to determine the quality of the DUT.
 13. The test system of claim11, wherein the controller is configured to determine a temperature atwhich the DUT has the limit value of the electrical parameter accordingto the model, and compare the temperature to the specified temperatureto determine the quality of the DUT.
 14. The test system of claim 11,wherein the controller is configured to control the interface accordingto a test flow that includes a plurality of parametric tests inserted ina sequence of other tests, and the interface is configured to measurethe electrical parameter of the DUT and the corresponding temperature inresponse to each of the parametric tests.
 15. The test system of claim11, wherein the controller is configured to determine the coefficientsin a pre-constructed polynomial model based on the measured values ofthe electrical parameter and corresponding temperatures.
 16. The testsystem of claim 11, wherein the interface is configured to receive froma temperature sensor in the DUT a sensed junction temperature.
 17. Thetest system of claim 11, wherein the interface is configured to measureat least one of an operating frequency, a current consumption and anoscillator frequency.
 18. The test system of claim 11, wherein theinterface is configured to measure an operating frequency of the DUT andthe corresponding temperature for a single time and determine thecoefficients in the pre-constructed model based on the measured value ofthe electrical parameter and the corresponding measured temperature. 19.A device that is tested as the DUT by the test system of claim
 11. 20. Amethod, comprising: constructing a model for modeling an electricalparameter of a device changing with a temperature, wherein the modelincludes a plurality of coefficients that are device-under-test (DUT)dependent variables; determining an integer number for which the integernumber of measurements of the electrical parameter and the correspondingtemperature provides a suitable indication of the device meeting theelectrical parameter at a specified temperature that is not measured;performing, for at least the integer number of times on a DUT, aparametric test measuring the electrical parameter and the correspondingtemperature; and ascertaining a quality of the DUT to meet a thresholdat a non-measured temperature based on the model and the parametrictest.